It's after the resignation of Edouard Philippe who has been in the post for three years.
Mr Castex, 55, is relatively unknown in France, although he is a senior civil servant.
The new Prime Minister has been a key player in the government's response to the Covid-19 pandemic.
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Haiti declares three days of national mourning for 25 killed in stampede
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Australia appoints woman to lead its army for the first time
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Orban ousted after 16 years as Hungarians flock to pro-EU rival
Hungary's veteran nationalist leader Viktor Orban lost power to the upstart centre-right Tisza party in Sunday's national election after 16 years in office, marking a setback for his allies in Russia and US President Donald Trump's White House.
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